The equation of the line in vector form passing through the point (−1,3,5) and parallel to line , z = 2. Is

Given: A line is passing through the point (−1,3,5) and parallel to line

To Find: The equation of the line in vector form.

The equation of a line passing through a point with position vector and parallel to vector is,

The line is parallel to the line , z = 2

So, the direction ratio of the given parallel line is = (2,3,0)

So, the direction vector is,

And the line is passing through the point (-1,3,5)

So, the point vector,

So, the vector form of the line is,